作者机构：
[Xu, Changjin; Xu, CJ] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liu, Zixin; Pang, Yicheng] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China.;[Shen, Jianwei] North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.
通讯机构：
[Xu, CJ ] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
关键词：
ergodic theory;markov Process;hessian matrix;Ito formula
摘要：
In the literature [16], the COVID-19 model has been constructed using deterministic approach. The present manuscript examines a stochastic model designed to capture the interplay between COVID-19 and varying infection rates on disease dynamics. We present the necessary criteria for a global solution to the considered model to exist and be unique. To illustrate several outcomes pertaining to the ergodic properties of the given system, the we utilize nonlinear analysis. Furthermore, the model undergoes simulation and is compared with deterministic dynamics. To verify the efficacy of the considered model and demonstrate its utility, we compare the dynamics of the infected population to real statistical data from multiple countries, such as the United Kingdom, Australia, Spain, and India. The proposed model has proven to be a reliable and effective tool for understanding the intricate nature of COVID-19 dynamics. Moreover, we provide a visually striking depiction of the impact of different infection rates on the propagation of the model under investigation. This visualization provides valuable insight into the multifaceted nature of the pandemic and significantly contributes to the comprehension of COVID-19 dynamics.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S,2024年0:0-0 ISSN：1937-1632
通讯作者：
Xu, CJ
作者机构：
[Xu, Changjin; Xu, CJ] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550025, Peoples R China.;[Cui, Qingyi; Pang, Yicheng; Ou, Wei] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Shen, Jianwei] North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R China.;[Baber, Muhammad zafarullah] Univ Lahore, Dept Math & Stat, Lahore, Pakistan.
通讯机构：
[Xu, CJ ] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550025, Peoples R China.
关键词：
Plankton population dynamical system;Hopf bifurcation;extended hybrid controller;stability;nonlinear delayed feedback controller;nature of solution
摘要：
Formulating suitable dynamical models to describe the interplay of different chemical substance in biology and chemistry is a very interesting topic. In this article, we set up a new plankton population dynamical system accompanying delay. Taking advantage of fixed point theorem and appropriate function, we derive the criteria on existence and uniqueness, boundedness of the solutions of the established plankton population dynamical system. By applying Hopf bifurcation and stability theorem of delayed dynamical system, we analyze the emergence of Hopf bifurcation and stability trait of the established plankton population dynamical system. Novel delay-independent criteria guaranteeing the emergence of Hopf bifurcation and stability of the system
期刊：
Fractal and Fractional,2023年7(2):142- ISSN：2504-3110
通讯作者：
Maoxin Liao
作者机构：
[Li, Weinan; Li, Bingbing; Liao, Maoxin; Chen, Huiwen] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
通讯机构：
[Maoxin Liao] S;School of Mathematics and Physics, University of South China, Hengyang 421001, China<&wdkj&>Author to whom correspondence should be addressed.
摘要：
In this paper, we study the stability and Hopf bifurcation of a class of six-neuron fractional BAM neural networks with multiple delays. Firstly, the model is transformed into a fractional neural network model with two nonidentical delays by using variable substitution. Then, by assigning a value to one of the time delays and selecting the remaining time delays as parameters, the critical value of Hopf bifurcation for different time delays is calculated. The study shows that when the time lag exceeds its critical value, the equilibrium point of the system will lose its stability and generate Hopf bifurcation. Finally, the correctness of theoretical analysis is verified by simulation.
期刊：
Communications in Nonlinear Science and Numerical Simulation,2023年118:107043 ISSN：1007-5704
通讯作者：
Changjin Xu
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Mu, Dan; Liu, Zixin; Pang, Yicheng] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Aouiti, Chaouki] Univ Carthage, Fac Sci Bizerta, UR13ES47 Res Units Math & Applicat, Bizerte 7021, Tunisia.
通讯机构：
[Changjin Xu] G;Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, PR China
关键词：
Boundedness;Delay;Existence and uniqueness;Fractional-order 4D neural networks;Hopf bifurcation;Stability
摘要：
Delay has a vital influence on the dynamics of neural networks. Exploring the effect of time delay on the dynamics of neural networks has become a hot issue in mathematics and engineering fields. In this current manuscript, on the basis of the earlier publications, we put forward a new fractional-order 4D neural networks incorporating two different time delays. First of all, the existence and uniqueness, boundedness of the solution of the fractional-order 4D neural networks incorporating two different time delays. are analyzed by applying contraction mapping principle, construct of an adaptive function, respectively. Next, the stability and the emergence of Hopf bifurcation are explored by making use of the stability and bifurcation theory of fractional-order dynamical system. A series of novel stability criteria and bifurcation conditions guaranteeing the stability and the emergence of Hopf bifurcation of the considered fractional-order 4D neural networks under the different delay cases are built. What,s more, the impact of delay on stabilizing neural networks and controlling the emergence of Hopf bifurcation of neural networks is adequately uncovered. At last, Matlab simulation figures are presented to confirm scientificness of the derived prime conclusions. The derived prime conclusions of this manuscript are perfectly innovative and own momentous theoretical reference value in the control issue and design aspect of neural networks.(c) 2022 Published by Elsevier B.V.
摘要：
In this paper, the stability and Hopf bifurcation of a six-neuron fractional BAM neural network model with multiple delays are considered. By transforming the multiple-delays model into a fractional-order neural network model with a delay through the variable substitution, we prove the conditions for the existence of Hopf bifurcation at the equilibrium point. Finally, our results are verified by numerical simulations.
摘要：
In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks.
期刊：
Expert Systems with Applications,2022年199:116859 ISSN：0957-4174
通讯作者：
Changjin Xu
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550025, Peoples R China.;[Xu, Changjin] Guizhou Key Lab Big Data Stat Anal, Guiyang 550025, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Yao, Lingyun] Guizhou Univ Finance & Econ, Guiyang 550025, Peoples R China.
通讯机构：
[Changjin Xu] G;Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, PR China<&wdkj&>Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang 550025, PR China
关键词：
Fractional-order bank data model;Global stability;Hopf bifurcation;Hopf bifurcation control;PDξ controller;Stability
期刊：
Fractal and Fractional,2021年5(4):257- ISSN：2504-3110
通讯作者：
Changjin Xu
作者机构：
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, China;Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang 550025, China;Author to whom correspondence should be addressed.;[Shang, Youlin; Li, Peiluan] School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, Hengyang 421001, China
通讯机构：
[Changjin Xu] G;Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, China<&wdkj&>Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang 550025, China<&wdkj&>Author to whom correspondence should be addressed.
